Phase-compensating networks



NovQlZ, 1929. H. NYQUIST ,73 ,05

PHASE COMPENSATING NETWORKS Original Filed Feb. 25, 1926. 2 Sheets-Sheet l fielay in serum .9 of Mm:

400 600 800 7000 I200 W I400 I500 1800 2000 I Cycles 02! 5200M BY ygw A TTORNEY Periods 175 Nov. 12, 1929. H. NYQUIST 1,735,052

' PHASE COMPENSATING NETWORKS Original Filed Feb. 25, 1926 2 Sheets-Sheet 2 ATTORNEYS.

Patented Nov. 12, 1929 UNITED STATES PATENT- OFFICE HARRY NYQUIST, OF MILLBURN, NEW JERSEY, ASSIGNOR TO AMERICAN TELEPHON AND TELEGRAPH COMPANY, A CORPORATION OF NEW YORK PHASE-COMPENSATING NETWORKS Original application filed February 25, 1926, Serial 110. 90,656. Divided and this application filed August 5, 1927.

of the current within a certain desired fre- "quency range will be in the same phase relation with one another at the receiving end as at the transmitting end. Another object of invention is to make the received composit wave' form in such a system of the same shape as the transmitted wave form. Another object is to provide for a desired displacement in time of the respective frequency components of a composite alternating current. Another object is to provide for a suitable phase shift of currents of-different frequencies in a circuit so as to bring them into a desired phase relation. Another object is to provide for a relative phase shift of the frequency components in a transmission line to compensate for a normal phase shift in the line and to restore the components at the receiving end of the line to the'same phase relation as though no line phase shift were present. Another object is to provide a transducer to operate intandem with a transmission line that'shall compensate the distortion due to differential phase shift on the line. Still another object is to provide a transducer to compensate for distortion due to a greater phase shift at high and low frequencies than at an intermediate frequency.- In the following specification with the accompanying drawings I disclose specific examples of practice according to my invention. It will be understood that the specification relates largely to these particular cases and that the invention is defined in the appended claims.

- By the word transducer as employed in this specification, I mean any apparatus .hav-

ing a pair of input terminals for applied electromotive force and a pair of output terminals by which electromotive force may be applied to another element, the output being a. function of the input.

Referring to the drawings, Figure 1 is a symbolic diagram of a four-wire transmis Serial No. 210,946.

sion system embodying my invention; Fig. 2 is a diagram of a general network of which special forms may be employed in embodying my invention; Fig. 3 is a diagram of a particular network used in an embodiment of my invention here disclosed by we of illustration; Fig. 4 is a diagram 0 delayfrequency characteristics to.- which reference will be made in explaining the principle of my invention, and the procedure for embodying it in a particular case; Fig. 5 is a diagram showing the relationv of my improved delay network to other elements of the system; Fig. 6 is a diagram showing delay as a function of frequency for certain transducers; Fig. 7 gives a family of delay -frequency characteristics that may afford guidance in the design of a suitable network in a particular case; Figs. 8 to 12, inclusive, show bridged-T network sections equivalent to Type C of Fig. 3; Figs. 13 and 13 Show bridged-T sections equivalent to Type B of Fig. 3; Figs. 13 and '13 show bridged-T 7 tenuation on the line. Voice frequency currents put on the line L gt station W go to the first repeater station, and then they pass through the phase distortion equalizer P which compensates for the differential retardation of the components of the various frequencies by further retarding them unequally so that they are brought to the same time relation to each other as at'the sending end. Then the currents pass through the attenuation equalizer E and then through the amplifier R, and so on at each repeater station. I will first assign specific values for the constants of a certain line and will give the specific design for the network of my invention in this instance, and thereafter I will discuss the principles on which this design is based and point out certain other examples of practice of the invention.

The line chosen for this first example is taken as a one-way No. 19 gauge medium heavy loaded, cable circuit, 154 miles long,

with a repeater-at the middle and at the receiving end, and with a phase compensating network at the receiving end. The constants of the loaded line are:

its full steady-state value he represented by the letter T. Thistime T as a function of frequency f is shown by the 'curve marked Lo'aded line in Fig. 1. It will beseen that the delay is greater for the higher frequencies of the essential voice range.

The appropriate phase equalizing network of Fig. 3 consists of sections of three different types, .eight sect-ions of Type A, six

sections of Type B and one section of Type.

C. All these sections are special cases of the general crossed or lattic network of Fig. 2.

The respective inductances and cat acities in the network of Fig. 3 have the va ues given in the following table:

- L =0.5 henry;' 0 02 microfarad;

' 0 0.1'micro arad;

- 111 0059 henry;

0 =0.024 microfarad;

0 =0.17 microfarad; v The eight sectionsofType A by themselves I have a delay-frequency characteristic as shown by the curve marked Type A in 4. \Vhen they are in tandem with the line,

the .resultant characteristic is shown by the dotted curve marked Line and Type A.

. It will be seen that the characteristic for the. loaded line'alone slopes up to the right and is concave tip, and the characteristic for the Type A network slopes down to the right and is concave up, and the resultant chara'cteristic shown in dotted lines ha'san intermediate minimum} The additional sections of Type B and Type C are designed so that, by themselves, they give intermediate maxima, as shown in Fig. 4, and the entire combination gives an approximately horizontal characteristic curve as designated Complete combination in Fig. 4. This means that for all the frequency components within the essen- A familiar formula of .etry is tial voice range the delay in transmission is approximately the same, that is, between about 0.021 and 0.022 second of time.

Referring to Fig. 5, let X be any transducer between the source G and the receiver Z. The delay-frequency characteristic of the transducer X over a certain frequency range will have a certain form, for example, as shown by the curve p in Fig. 6. Suppose it is desired that the currents shall go to receiver '-Z with their components of different frequency in the same time relation as at the generator G, in other words, so that all the components will be delayed equally and at the receiver the delay-frequency curve will be a horizontal line such as g. This effect will be obtained by interposing a compensator whose characteristic 7 is complementary to p as shown in Fig. 6.

If the characteristic of the transducer X slopes up to the right as at p in Fig. 6, then the compensator Y should have a characteristic sloping down to the right as at 1'. Sections of crossed type network, such as those of Type A in Fig. 3, answer to this requirement, as will be seen by comparing curve 1' in Fig. 6 with the curve for Type A in Fig. 4.

For aseries of network sections like the one shown generally in-Fig. 2, and with the impedance values indicated thereon, the propagation constant I and the characteristic impedance K are mulas;

It is desirable that the characteristic impedance shall be a real constant K, and ap- I proximately the same as the impedance (resistance) of the elements with which the network is oonnectcd on the input and output sides. Assuming that the impedances z, and

.2 are dissipationless, that is made up only of reactance elements, this result is secured by making 2 15.2 and z =K/z where K is a real constant and where z is a pure reactance. A network of the type of Fig. 2 with K constant is called a constant K network. Substituting in 1, it follows that cosh I=1+ (4) hyperbolic trigonom- I cosh P- 1 A t p m (5) Substituting from 4), this reduces to tanh I f/2=z/2. (6) In general, the propagation constant I may given by the following for be put equal to a-H'B, where a is the attenuation constant and fi is the phase shift con stant. The structure for z is of reactance elements only and on this basisit follows from equation (6) that a= and that 2' tan ,8/2=2/2. (7)

For the sections of Type A of Fig. 3, this gives 6 2 tan If; It is approximately true that Hence by differentiating (8), the result is obtained that By the aid of this equation, delay frequency characteristics can be drawn for respective values of the product L G, and from them it can readily be determined what is the best value of G and how many network sections are necessary toget such compensation as should be efiective for the Type Asections.

In this way, the number of sections for Type- A in Fig. 3 has been fixed at eight, and the value of L G at 10. The value of L and the dependent value of C have been deter- I circuit so that mined so that w/Lf/ equals the desired value of K, 1580 ohms.

For the sections of Type B or C, let the impedance 2 be made up of a series'resonant where w=21rf, f being the frequency, and b and 10 are parameters to which we may assign proper values, 10 /271 f being .the resonance frequency. For the Type B network,

and the truth of Equation (11) will become apparent on noticing that w l/ /L O and substituting for L and C in terms of b and 10 in the equation The truth of Equation (11) will become apparent'in'this case by substituting for L and C in terms of b and;w in the equation iwL +1/iw0 iwb /EC; 2K" 2 ai /L 0, As before, with 1=a+i,8, from Equations (6) and- (11)it follows that tanh I/2= tanh 2' 5/2 (db/2) (w/cu w /w) (l2) whence B=2tan' (b/2) (w/w w /w) (13) Differentiating (13) and substituting in (9),

M l (we w/w0w0/w (14 As w increases from O to infinity, the numerator decreases always, but the denominator passes through a minimum at 10 10 If I) is made sufficiently large, the fraction in (14) has a maximum near w This is shown in Fig. 7, which also shows that by giving to b increasing values, T can be made to increase at its maximum with accompanying decrease of values away from its maximum, the area of the curve remaining constant. By increasing the number of sections of the network, T can be increased over the whole range for .11). Furthermore, w, maybe chosen to put the maximum point at the right orleft as may be desired.

Referring to Fig. 4, it is seen that after the compensation efi'ected'by Type A, this gives a minimum at or near i000 cycles, or w =21r1000. In Fig. 7 a series of curves is constructed with coordinates f/f and Tf instead of coordinates f and T as in Fig. 4;

This is somewhat more convenient, and the curves of Fig. 7 can be utllized for any value of 10,. Plotted either way, the area of each f. b bw Also,

' z'2wK shunt v 0, b/QKw shunt 1, QK/bw, In Type B since I) =2,

shunt 0,=1/Kw shunt L =K/w and in Type C,

It will be noticed that the valueb=2 enables us to use inductances and capacities of the same values in the series and shunt combinaresultant characteristic as- It hasalready been mentioned that each section of Type B or Type C contributes about aunit area to the curves of Figs. 4oz 7. Each Type A section contributes only about half a unit, but this is not necessarily to be looked on as a disadvantage, for the Type Asections have only half as many reactance elements asthe others. 7

The general procedure is first to-plot the delay-frequency characteristic of the transducerto be compensated asinthe case of the curve marked Loaded line in Fig. 4.] Then add sections like Type A in proper number and with properly'chosen reactance values so as tobring the endsjof the characteristic up somewhere nearly to the same level. Then add sections like Type B or to raise the minimum dips in thecurve, up to nearly thelevel of the ends, and make the curve have nearl' the same altitudeall across the essential curve of Fig.

Reterrlng again tion of Type B or Type C contributes about .a unit-of area to the r'esu ltant'curve. of F ig. 4 or Fig. 7, (andhalf aunit for each secto the fact that each secrequency range, as for the uppermost v 1 9 can readily be realized physically in the tion of Type A) it will readily be seen that- 3." guide. as to the number of sections'thatmay-need to be employed. Having-given' the loaded line curve'fof Fig.

7 r 4;, an ideal characteristic can b'e'drawn higher I up'an'd the area between the two character- 'i,s ticswill give the number of sections of network that must be employed. The shorter the frequency range is made, the less the number .of sections that will be required, but shortening the frequency range may imr [pair-the 'q'uality in onew'ay' while the addiimpr'ov'es it in another way. Assuming that economy of apparatus, particularly'petw'ork sect1ons,. is 1a desideratum, then it"may be said that -witliout unduly shortening the frea little trom the horizontal, and will require nozmore network sections than would r be required to get aiully liorizontalcharactristic T0 R13."leSS'fIfeqUBIlCy range. In

other words, starting with a; characteristic 1 like that marked loadedline the optimum the legends of Fig. 8 as maaoea work sections will .bea characteristic-which extends over the whole desired frequency range but which slopes up a little at the right and thus requires a less number of network sections than would be necessary to attain a completely horizontal characteristic'over the same frequency range. I have discovered that certain economies and other advantages are possible in the design and construction of'diiferential phase compensators' by use of modifications which re uire a smaller number of elements and yet w ich yield structures possessing the same flexibility or number of degrees of freedom as is present inflthe lattice structures of F igr3.

Some of these modifications are shown in.

.the application notedabove, of which this application is a division and ofthose there shown certain ones are included herein.

I .l1ave found that the bridged-T network section of F ig. 8 is equivalent to the lattice Type C network section'of 3. The equlv- 'alence is dependent upon giving the re- ..ac-tanceelements' the values indicated by 7 compared with Type C of Fig. 3.

In Fig. 9 a substitution'is made for the two coils of Fig. 8 having mutual inductance, and a system of three'equivalent coils is *introduced with no mutual inductance. be-

tween the members. One of thesecoils has a negative inductancev which, of course, has no physical counterpart. But provided that L is greater than L the network of Fig.

network of FigJlO.

Fig. 11 is derived from Fig. 10 by the well-" known substitution of a delta for the star I connection.

Another equivalent for Fig. 10 is obtained 1n Fig. 112 by substituting for the star a proper inductance values to transformer of 1 be the equivalent of the star.

- advantage' over Type C of F ig'. 3 in that tion of phase correcting network sections characteristic with proper economy of not-- from Fig. 12,

has the practical advantagethat the total-number of coilshas been reduced v 4-to, 2 and the total number of 0011- 'denser s has been reduced from-4 to 2. r In only a single coil is used; subject to the condition that it has an inductance coupling less than unity, and thus it em bodies two magnetic circuits and "is theoret-ically tlieequivalnt of two coils. Fig. 13 the two coils are equal and separate, which simplifies construction and design;

Fig. 13 is 'analternative, equivalent for Fig. 13 1and..Eigs. 13) and 13 are further eq'uivallentsior; Type (1 of Fig. 3.

fade' equal to L4, theneach of rhe'ibrid ed-T network a Fig. 8 has the of compensation at an intermediate frequency,

"phase compensator consisting of sections,

some of which compensate most for the lower frequencies of the, essential voice frequency range, and others of which give a maximum of compensation at 'an intermediate frequency, at least one of said sections being of bridged-T type.

4:. In combination, a loaded line and a phase compensator consisting of sections, some of which compensate most for the lower frequencies of the essential voice frequency range, and others of which give a maximum the sections being of the bridged-T type."

5, In combination, a transducer giving different delays for different frequencies over a certain frequency range anda delay compensator consisting of bridged-T network sections, the values of the inductances and capacities thereof being determined by the inducta'nces and capacities of an equivalent lattice type network.

6.- In combination, a transducer giving different delays for different frequencies over a certain frequency range and a delay compensator consisting of bridged-T network sections, at least one of these sections giving a maximum of delay within said frequency range, the bridging member for the sections comprising an inductance,

7. In combination, a transducer giving different delays for different frequencies over a certain frequency range, and a delay compensator comprising one or more sections of bridged-'3 networks and having the same delay characteristic as a plurality of sections of lattice type network and retaining the samedegree of flexibility as the lattice net work, but consolidated to a smaller number of elements.

8. In combination, a transducer giving different delays for different frequencies over a certain frequency range and a delay com pensator in combination therewith, said delay compensator comprising at least one section of a bridged-T network and composed of a certain.- number of reactance elements,

the said reactance elements being adjusted in value to make the delay frequency characteristic of the compensator the same as of a series of lattice type network sections com- August, 1927.

posed of a greater number of reactance elements and designed to compensate the delay in the said transducer.

In testimony whereof, I have signed my name to this specification this 2nd day of HARRY NYQUIST. 

